Hydrol. Earth Syst. Sci., 14, 1465–1476, 2010
www.hydrol-earth-syst-sci.net/14/1465/2010/
doi:10.5194/hess-14-1465-2010
© Author(s) 2010. CC Attribution 3.0 License.
Hydrology and
Earth System
Sciences
Using flushing rate to investigate spring-neap and spatial variations
of gravitational circulation and tidal exchanges in an estuary
D. C. Shaha1 , Y.-K. Cho1 , G.-H. Seo1 , C.-S. Kim1 , and K. T. Jung2
1 Department
2 Korea
of Oceanography, Chonnam National University, Gwangju 500–757, Korea
Ocean Research and Development Institute, Ansan 426–744, Korea
Received: 6 February 2010 – Published in Hydrol. Earth Syst. Sci. Discuss.: 2 March 2010
Revised: 21 July 2010 – Accepted: 26 July 2010 – Published: 5 August 2010
Abstract. Spring-neap and spatial variations of gravitational
circulation and tidal exchanges in the Sumjin River Estuary
(SRE) were investigated using the flushing rate. The flushing rate was calculated between multiple estuarine segments
and the adjacent bay to examine the spatial variation of two
exchanges. The strength of gravitational circulation and tidal
exchanges modulated significantly between spring and neap
tides, where stratification alternated between well-mixed and
highly-stratified conditions over the spring-neap cycle. Tidedriven dispersive flux of salt dominated over gravitational
circulation exchange near the mouth during spring tide due to
the larger tidal amplitude that caused well-mixed conditions
and rapid exchange. In contrast, the central and inner regimes
were found to be partially stratified during spring tide due to
the reduction in tidal amplitude where both gravitational circulation and tidal exchanges were important in transporting
salt. The combined contributions of two fluxes were also
found during neap tide along the SRE due to the significant
reduction in vertical mixing that accompanied strong stratification. Gravitational circulation exchange almost entirely
dominated in transporting salt at the upstream end during
spring and neap tides.
1
Introduction
The net flow of water into and out of estuaries influences
the exchanges with the surrounding coastal region, thus playing a role in controlling the estuarine environment by regulating the transport of nutrients, sediments, organisms and
pollutants. Therefore, it is essential to understand estuarine
hydrodynamic processes, such as tidal exchange and gravitational circulation exchange or some combination of the
Correspondence to: Y.-K. Cho
([email protected])
two, which transport water and its constituents (Monsen et
al., 2002; Ribeiro et al., 2004). The tidal exchange is more
or less independent of the river discharge, whereas the gravitational circulation exchange is strongly dependent on the
freshwater input in maintaining the longitudinal density gradient that controls an exchange flow, with seaward flow at the
surface and landward flow at depth (Officer and Kester, 1991;
Dyer, 1997). The competition between tidally induced vertical mixing and river generated buoyancy is the main factor
determining the differences in water exchange.
Spring-neap variations in tidal shear stress may result in
spring-neap variations in tidally driven mixing, stratification and gravitational circulation (Jay and Smith, 1990; Uncles and Stephens, 1996; Monismith et al., 1996; Ribeiro et
al., 2004; Savenije, 2005). Tide-driven shear mechanisms
dominate in narrow, shallow estuaries, and strong tidal currents tend to suppress stratification through vigorous mixing, which inhibits gravitational circulation (West and Broyd,
1981; Uncles et al., 1985; Geyer, 1993; Savenije, 2005).
However, the weaker turbulence during a neap tide could lead
to an acceleration of gravitational circulation (Nunes Vaz et
al., 1989; Monismith et al., 1996). Such influence of low
mixing at neap tides is noted by Jay and Smith (1990) in the
extent of salt intrusion into the Columbia River Estuary.
Gravitational circulation is the most efficient mechanism
for flushing river-borne pollutants out to the open sea (Nunes
Vaz et al., 1989). In general gravitational circulation increases in strength with increasing river flow (Nguyen et al.,
2008), which may cause a depletion of estuarine resident
populations by advection from their resident position, particularly larval forms of bottom feeders and deep-water organisms, but also copepods and larval fish (Hough and Naylor,
1991; Jassby et al., 1995; Morgan et al., 1997, Kimmerer
et al., 1998, 2002; Monismith et al., 2002). Recently, the
spatiotemporal variations on the abundance of the demersal
copepod, Pseudodiaptomus sp., in the Sumjin River Estuary
(SRE) have been reported (Park et al., 2005). However, there
Published by Copernicus Publications on behalf of the European Geosciences Union.
1466
D. C. Shaha et al.: Flushing rate for gravitational circulation and tidal exchanges
has been no information on the physical aspects of the tidal
exchange and gravitational circulation exchange for the SRE.
Officer and Kester (1991) use the flushing rate to understand estuarine hydrodynamics and transfer processes that is
related to the tidal exchange and gravitational circulation exchange. They calculate single flushing rate for the entire estuarine system. However, Monsen et al. (2002) reported that
no single flushing rate for a system is valid for all time periods, locations and constituents, and it does not describe all
transport processes. In addition, single flushing rate provides
no information about the connections between transport and
spatial heterogeneity of non-conservative quantities, such as
specific conductivity, temperature and chlorophyll-a. As a
single flushing rate does not represent the spatial variation
of all transport processes, the flushing rate method was applied to multiple segments of the SRE to examine the spatial
variability of flushing rate and to estimate gravitational circulation and tidal exchanges.
The main focuses of this study are i) to understand the spatial variation of gravitational circulation exchange and tidal
exchange between multiple segments of the SRE and the adjacent bay during spring and neap tides on the basis of the
flushing rate and; ii) to suggest the flushing rate as an useful
parameter to investigate the relative contribution of the tidal
exchange and gravitational circulation exchange in transporting salt up-estuary.
The rest of this paper is organized as follows. The data
sources are briefly presented in Sect. 2. The methodology is
described in Sect. 3. The results are presented in Sect. 4. A
discussion follows in Sect. 5, with the conclusions in Sect. 6.
2
Study area and data
The SRE is one of the few natural estuaries on the south
coast of Korea. The watershed area, including farmland,
is 4897 km2 . The Sumjin River discharges into Gwangyang
bay. The bay is connected in the south to the coastal ocean
(South Sea) and in the east to Jinju bay via the narrow Noryang Channel (Fig. 1). The climate of Korea is characterized by four distinct seasons: spring (March, April, May),
summer (June, July, August), autumn (September, October,
November) and winter (December, January, February). The
mean precipitation is 1418 mm a−1 , based on annual data
from 1968 to 2001. Seasonal precipitation and runoff in the
Sumjin River basin have decreased in spring and winter, but
increased in summer (Bae et al. 2008). The tidal cycle is
semi-diurnal, with mean spring and neap ranges of 3.33 and
1.02 m, respectively.
The river discharge data used in this study were from
the Songjung gauge station, located about 11 km upstream
from CTD (conductivity-temperature-depth) station 24 operated by the Ministry of Construction and Transportation. The maximum monthly median river discharge was
highest (370 m3 s−1 ) in July 2006 and lowest (11 m3 s−1 )
Hydrol. Earth Syst. Sci., 14, 1465–1476, 2010
Fig. 1. Map of the study area. The solid circles indicate the CTD
stations. The star mark denotes the locations of the Gwangyang
(GT1 and GT2) and Hadong (HT) tidal stations.
Table 1. Observed tidal amplitudes for M2 , S2 , K1 and O1 at the
Gwangyang and Hadong tidal stations.
Amplitude (cm)
Tidal station
Gwangyang (GT2)
Hadong (HT)
M2
S2
K1
O1
109.3
96.6
46.7
42.8
18.7
17.9
14.3
11.9
in January 2005. Tidal constituents for Gwangyang bay
(GT2, Fig. 1) were obtained from the Korean Ocean
Research & Development Institute (http://www.kordi.re.kr/
odmd/harmonic2004/). The M2 tide is the primary tidal constituent at the river mouth. Sea level data for 2005 and 2006
from Hadong tidal (HT) gauge station (http://www.wamis.
go.kr/wkw/WL DUBWLOBS.ASPX) were analyzed using
the Task-2000 tidal package developed by the Proudman
Oceanographic Laboratory (Bell et al., 1999). The major
tidal constituents (M2 , S2 , K1 , O1 ) are shown in Table 1. The
tidal amplitudes of the M2 and S2 constituents were found to
decrease to 12 and 8% within the estuary at HT, respectively.
Time-series observations of the salinity distribution were
conducted over a tidal cycle during spring tide at station 7 on
21–22 July 2005 and on 15–16 June 2006. The longitudinal
transects for salinity and temperature were carried out at high
water during both spring and neap tides during each season
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D. C. Shaha et al.: Flushing rate for gravitational circulation and tidal exchanges
1467
from August 2004 to April 2007 using a CTD profiler (Ocean
Seven 304 of IDRONAUT Company). A Global Positioning
System was used to obtain the locations of the CTD stations
(Fig. 1). The nominal distance between the CTD stations was
1 km. The measurements were started from the river mouth
one and half hour before high water, and took about one and
half hour to complete. On the basis of the stratification parameter, which is the ratio of the difference in salinity between the surface and bottom divided by the depth averaged
salinity, well-mixed conditions were found near the mouth of
the SRE, with partially-mixed conditions in the central and
inner regimes during spring tide. In contrast, strong stratified conditions were found along the SRE during neap tide
(Shaha and Cho, 2009).
3
Fig. 2. Salinities observed at 8 km far from the mouth of the Sumjin
River Estuary as a function of river discharge.
Methods
The flushing rate (F ) is defined as the rate at which the index
quantity is exchanged between multiple estuarine segments
and the adjacent sea (Officer and Kester, 1991; Dyer, 1997).
Officer and Kester (1991) have calculated single flushing rate
near the mouth of Narragansett bay using average bay salinity to understand hydrodynamics and transport processes. A
single flushing rate for the whole system does not describe
the spatial variation of tidal exchange and gravitational circulation exchange. To calculate the flushing rate between
multiple estuarine segments and the adjacent bay, the salt
balance equation at steady state condition can be used as follows (Bowden and Gilligan, 1971; Savenije, 1993; Smith and
Hollibaugh, 2006; Nguyen et al., 2008).
RS − AD
∂S
=0
∂x
(1)
where S is the salinity, A is the tidal average cross-sectional
area and R represents the river discharge associated with
K
residual flow. D is the dispersion coefficient DD0 = SS0
where the subscript 0 refers to the situation at x = 0 and K
is the dimensionless coefficient which is larger than zero
(Savenije, 1993). The dispersion coefficient D has a large
value near the mouth of estuaries, decreasing gradually in
the upstream direction to become zero at the toe of salt intrusion curve. This relation adequately describes a combination
of density-driven (also called gravitational circulation) and
tide-driven dispersion (Savenije, 1993; Nguyen et al., 2008).
The flushing rate F is then given for a single-layer system
with multiple segments:
RSmi − Fi (S0 − Si ) = 0
Fi =
with F =AD/1x
RSmi
S0 − Si
(2)
(3)
Smi is the salinity of the residual flow assumed at the boundary between the segment of interest and the adjacent source
segment (usually the oceanic end member of the estuary).
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Smith and Hollibaugh (2006) suggested that this salinity can
be estimated as the average of those two segments, Smi =
(S0 +Si )/2. S0 is the salinity of the adjacent bay (oceanic end
member of the SRE) and Si is the segment salinity of interest. The term (S0 −Si ) is the box (segment) model equivalent
of the horizontal salinity difference (Smith and Hollibaugh,
2006). If there is a measurable salinity difference between
the segment of interest and the adjacent segment (s), Eq. (3)
can be solved for exchange flow between many segments and
the adjacent bay (Smith and Hollibaugh, 2006). When the
salinity difference between the segments becomes small and
indistinguishable from 0, this equation can not be solved for
exchange flow because negative F has no physical meaning.
To apply a steady state model in an estuary, it is necessary
to examine how quickly the system adjusts to a new situation. If the time required for reaching the system in a new
equilibrium is too long, a steady state model can not be used
(Savenije, 2005). The residence time of the SRE varied from
3.6 days for the river discharge of 77 m3 s−1 to 13.5 days for
the river discharge of 10 m3 s−1 , with an average of 7.3 and
7.5 days, during spring and neap tide, respectively. In view
of the short residence time, SRE can be considered to be near
steady state. Salinity versus river discharge relationships can
also be used to make a validation of steady state approximations (Regnier et al., 1998). In that case, the solution of
salinity versus river discharge should be unique at any position along a steady state estuarine system. Figure 2 shows
the yearly evolution of salinity observed at CTD station 8
with various river discharges in the SRE. The approximate
homogeneity in salinity was observed for the same river flow
which also implies the steady state condition of the SRE.
The quantity F (L3 T−1 ) represents the combined effects
of the tide-driven exchange and the gravitational circulation exchange, which equals the total longitudinal flux in
the Hansen-Rattray estuarine parameter ν (Hansen and RatHydrol. Earth Syst. Sci., 14, 1465–1476, 2010
1468
D. C. Shaha et al.: Flushing rate for gravitational circulation and tidal exchanges
tray, 1965, 1966). F is used to quantify gravitational circulation exchange and tidal exchange. A plot of F versus R illustrates which exchange process is responsible in
transporting salt into the system: (1) tidal exchange should
be independent of the river discharge, but the gravitational
circulation exchange should depend strongly on it (Officer
and Kester, 1991; Dyer, 1997). If the tidal exchange is
dominant over the gravitational circulation, then the flushing rate (F ) should be about constant for all river discharges
(Dyer, 1997). This indicates that the total salt transport is
caused entirely by tidal exchange and gravitational convection ceases i.e. mixing is dominant over advection. (2) if
there were no tidal exchange, a plot of F against R would
give a curve with an intercept at zero and increasing values
of F for increasing values of R (Dyer, 1997). In that case,
the tide-driven dispersive flux of salt is unimportant and upestuary salt transport is entirely dominated by gravitational
exchange. Shaha and Cho (2009) found that gravitational
circulation was much more effective than tide-driven dispersion in distributing an isohaline of 1 psu at the upstream end
of the SRE. (3) If both tidal exchange and gravitational circulation are active, the plot of the flushing rate against the river
discharge should have an intercept value (Fint ) at zero river
flow, which represents the tidal exchange, and the amounts in
excess of the intercept value for various river discharge conditions represent the gravitational circulation exchange (Gc )
(Officer and Kester, 1991; Dyer, 1997). In such condition,
the salt transport has contributions from both tide-driven and
density-driven processes. Thus, the transport of salt downstream by the river discharge is the sum of the gravitational
circulation flux (Gc ) and tide-driven dispersive flux (Fint ).
The tide-driven exchanges are dominant over gravitational
circulation exchanges if Fint > Gc , and the gravitational circulation exchanges over tide-driven exchanges if Fint < Gc
for a specific river discharge. The tide-driven dispersive flux
of salt exceeds the gravitational flux during a period of decreasing freshwater input (Pilson, 1985; Fram et al., 2007;
Nguyen et al., 2008).
The estuarine parameter ν is the proportion of the tidedriven fraction (Fint ) to the total upstream salt flux (F =
Fint + Gc ) in an estuary given by Officer and Kester (1991)
and Dyer (1997).
νi =
Finti
Fi
(4)
If ν approaches 1, the upstream transport of salt is entirely
dominated by tide-driven processes. If ν is close to 0, upestuary salt transport is almost entirely by gravitational circulation. If 0.1 < ν < 0.9, the system experiences a contribution of both gravitational circulation and tide-driven circulation to the upstream salt transport (Hansen and Rattray, 1966;
Valle-Levinson, 2010).
Equation (3) implies that the system is well mixed. However, the SRE shows relatively strong stratification during
neap tide and well mixed condition with weak vertical salinHydrol. Earth Syst. Sci., 14, 1465–1476, 2010
ity gradients during spring tide (Shaha and Cho, 2009).
Therefore, the flushing rate has been calculated using Eq. (3)
for spring tide considering the system as single layer with
multiple segments. In contrast, the flushing rate equation
has been modified for two layer circulation during neap tide
with multiple segments. For two-layer circulation analytical
protocol of Gordon et al. (1996) is followed to calculate the
flushing rate.
A steady state in which volume is conserved has volume
fluxes
Qsi = Qbi + R = Fi
(5)
The oceanic water enters the bottom layer; flows upward
(Qbi ) into the surface layer and out (Qsi = Fi ) to the ocean.
The volume of outflow is associated with freshwater inputs.
If salt flux through the mouth is dominated by the exchange flux, then the net salt balance is
Qsi Ssi = Qbi Sbi
(6)
where Sbi is the bottom salinity and Ssi is the surface salinity
of each segment. The inflow from the oceanic end member to
the segment of interest through boundary (i = 1...12) reads
the following.
Qbi =
RSsi
Sbi − Ssi
(7)
Flushing rate is then given for two-layer system with multiple
segments:
Fi =
si−1
R Ssi +S
2
+R
Sbi − Ssi
(8)
Equation (8) can be solved for exchange flow between many
segments and the adjacent bay only if there is a salinity difference between the bottom salinity (Sbi ) and the surface
salinity (Ssi ). As the SRE is stratified during neap tide,
the salinity of the upper stratified layer was averaged to obtain Ssi . In this study, the bottom salinity is considered as
Sb0 (= Sb1 = ... = Sb10 ). Landward of 18 km depth average
salinity is used to calculate flushing rate considering the system as one layer due to the absent of two layer circulation.
To obtain more accurate estimation of the flushing rate at
the boundary between segments, the SRE was divided into
twelve segments, with 2 km in length. The segmentation provides a box model approximation of the longitudinal salinity
gradients. The flushing rate was calculated between multiple
estuarine segments and the adjacent bay in response to the
daily average freshwater input. Two CTD stations were allocated for each segment to obtain average salinity (Si ) of that
segment. The salinity of the seawater entering the SRE via
Gwangyang bay varied with time. The CTD station 1 was
treated as the seaward boundary for reference salinity of the
seawater (Sb0 ) entering in the bottom and Ssi of the seawater
surface salinity near the mouth.
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D. C. Shaha et al.: Flushing rate for gravitational circulation and tidal exchanges
1469
Fig. 4. Salinity distributions for all longitudinal depth surveys of the
Sumjin River Estuary at high water during spring (a, b) and neap (c,
d) tides during summer and autumn of 2004. The black solid circles
indicate the CTD stations.
Fig. 3. Time-depth distributions of the salinity profile during spring
tide, with low river discharge (28 m3 s−1 ) on 21–22 July 2005 (a),
and with high river discharge (120 m3 s−1 ) on 15–16 June 2006 (b)
over a tidal cycle at station 7.
4
4.1
Results
Diurnal variation of salinity
A time-series of salinity was observed over a tidal cycle during spring tide at CTD station 7 on 21–22 July 2005 and on
15–16 June 2006. The mean river discharges over the M2
tidal cycle were 28 and 120 m3 s−1 in 2005 and 2006, respectively. During high tide, a salinity of 27 psu was found
at the observation point both in 2005 and 2006 (Fig. 3a–b)
and the high tide heights were 3.8 and 3.6 m in 2005 and
2006, respectively. Comparing two distributions with each
other, it appeared that the buoyancy force as a freshwater input was the main differentiating factor. Although the river
discharge was 77% larger in 2006 than that in July 2005, the
increased river discharge did not hinder the inflow of 27 psu
salt wedge from Gwangyang bay to the observation point but
increased the vertical salinity gradient of 50%. The difference in salinity between two subsequent high tides was approximately 3 psu. As the high water height differences between two subsequent high tides were 0.71 m in 2005 and
0.67 m in 2006, this difference might cause that variation.
4.2
Longitudinal variation of salinity
Tide and river discharge are two main forcing factors controlling estuarine circulation (deCastro et al., 2004; Savenije,
2005; Ji, 2008). Changes in the tidal currents with the springneap tidal cycle can result in fortnightly modulation of stratification and gravitational circulation (Simpson et al., 1990;
Ribeiro et al., 2004). Longitudinal transects of salinity were
carried out at high water during both spring and neap tides in
each season from August 2004 to April 2007. The vertical
www.hydrol-earth-syst-sci.net/14/1465/2010/
Fig. 5. Salinity distributions for all longitudinal depth surveys of
the Sumjin River Estuary at high water during spring (a, b, c, d)
and neap (e, f, g, h) tides in each season of 2005. The black solid
circles indicate the CTD stations.
sections showed a relatively well mixed to partially mixed
structure during spring tide (Figs. 4 and 5). The highest
saline water of 33 psu appeared at the lower portion of the estuary over the entire observation periods during spring, 2005
(Fig. 5b). In addition, an isolated structure of saline water
appeared about 9 km upstream from the mouth (Fig. 5d, g
and h). This phenomenon may have occurred due to mixing
between seawater and freshwater inflow from the tributary
(Hwangchon), as the density structure is largely controlled
by the freshwater input in the coastal water and the density
structure followed that salinity distribution. The vertical sections of salinity (2006, 2007) during spring and neap tides
have not been shown here owing to their similar structures.
Hydrol. Earth Syst. Sci., 14, 1465–1476, 2010
1470
D. C. Shaha et al.: Flushing rate for gravitational circulation and tidal exchanges
Fig. 6. Schematic diagram illustrating the calculation of flushing rate at the boundary between two adjacent segments for well and partially
mixed condition during spring tide (upper) and for stratified condition during neap tide (lower) with low (10 and 11 m3 s−1 ) and high (50 and
44 m3 s−1 ) river discharges (R). In two layer system during neap tide, the outflow (Fi ) from the surface layer to the ocean through boundary
is the sum of deep flow volume (Qbi ) plus river discharge.
Strong stratification appeared during neap tide in all seasons (Figs. 4 and 5). As the tidal amplitude decreased during neap tide, the weakened effect of the bottom friction
strengthens the gravitational circulation, causing strong stratification. Strong stratification and gravitational circulation
during neap tide was noted by Monismith et al. (1996) in
Northern San Francisco bay. On the basis of the stratification parameter, the SRE transitions from partially or wellmixed during spring tide to stratified during neap tide (Shaha
and Cho, 2009). In general, the strength of stratification was
comparatively increased in summer due to the high river discharge (77 m3 s−1 ) than other seasons (Fig. 5g).
4.3
Spring-neap and spatial variations of gravitational
circulation exchange and tide-driven exchange
To investigate the spatial variations in gravitational circulation exchange and tide-driven exchange during spring and
neap tides, the flushing rate was calculated at twelve boundaries starting from the oceanic end member to upstream end
by dividing the SRE into twelve segments. The schematic diagram (Fig. 6) illustrates the calculation of flushing rate for
well and partially mixed condition during spring tide (upper)
and for stratified condition during neap tide (lower) with low
and high river discharge (R) conditions. At low river discharge condition during spring tide (neap tide), the flushing
rate increased by a factor of 100 (9) from the upstream end to
the mouth of the SRE. At high river discharge during spring
tide (neap), the flushing rate increased by a factor of 23 (5)
from the upstream end to the mouth of the SRE. Figure 7
shows the spatial variations of the mean flushing rate during
Hydrol. Earth Syst. Sci., 14, 1465–1476, 2010
Fig. 7. Spatial variation of the mean flushing rate (m3 s−1 ) during
spring and neap tides.
spring and neap tides. The mean flushing rate was extremely
heterogeneous, ranging from 13 to 842 m3 s−1 . The standard deviation became very large at the oceanic end member
as the denominator of Eqs. (3) and (8) approached to about
zero. The small fluctuation of this denominator yielded very
sparse flushing rate near the mouth which caused large scale
standard deviation. The flushing rate was approximately four
times greater near the mouth during spring tide due to the
larger tidal amplitude than during neap tide. The flushing
rate varied significantly between spring and neap tides landward of 7 km from the mouth of the SRE. This length is consistent with the observed median tidal excursion length of
6.8 km (Shaha and Cho, 2009). The higher the flushing rate,
the more efficient the downstream of the SRE is to flush out.
Landward of 8 km the flushing rates were approximately the
same during spring and neap tides due to decreasing tidal effects in the central and inner regimes (Table 1).
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D. C. Shaha et al.: Flushing rate for gravitational circulation and tidal exchanges
1471
Table 2. Volume average salinity (S) for the Sumjin River Estuary, ocean salinity (S0 ), and river discharges (R) for various periods of the
year along with calculated flushing rate (F ) during spring and neap tides.
Spring
Neap
R (m3 s−1 )
S
S0
F (m3 s−1 )
R (m3 s−1 )
S
S0
F (m3 s−1 )
46
29
10
18
58
16
20
11
50
9
12
21
15.42
16.92
20.27
21.17
14.59
16.27
20.92
24.45
12.45
22.20
25.88
18.87
31.46
31.16
32.43
33.57
30.46
31.59
32.55
33.51
30.00
31.83
32.94
32.95
90.20
63.48
26.67
48.75
111.32
32.98
56.00
40.69
85.47
29.75
56.03
49.14
26
22
16
26
77
13
14
30
44
15
11
14
17.75
18.42
20.10
12.36
9.29
19.44
19.20
16.22
12.80
19.75
19.97
17.88
32.07
31.02
32.82
32.36
30.61
31.58
32.73
33.16
29.24
31.08
32.71
32.83
58.22
54.14
41.26
42.07
110.57
33.81
33.88
58.72
78.25
41.15
28.23
30.74
Fig. 8. Plot of the flushing rate (F ) calculated for the average salinity of the Sumjin River Estuary against the river discharge (R) during spring and neap tides. The intercept value, Fint , denotes the
tide-driven exchange. The amounts in excess of Fint for the various river discharges indicate the gravitational circulation exchange
(Gc ).
Volume average salinity (S) for the SRE, ocean salinity
(S0 ), and river discharges (R) for various periods of the year
along with calculated flushing rate (F ) during spring and
neap tides are given in Table 2. Figure 8 is a plot of flushing rate for the average salinity of the SRE, which is a single flushing rate, versus the river discharge during spring
and neap tides. This represented a combined effect of the
tide-driven exchange and gravitational circulation exchange
in transporting salt upstream. The intercept value (Fint ) provides the tidal exchange whereas the amounts in excess of the
intercept value (here expressed by Gc ) for various river discharge conditions give the gravitational circulation exchange.
Tide-driven dispersive flux of salt exceeded gravitational circulation flux at river discharge of <20 m3 s−1 . This combined effect depicts only the general exchange characteristics
of the SRE without differentiating spatial variations. Such
combined effect was noted by Officer and Kester (1991) for
the entire Narragansett bay.
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To understand the spatial variations in the tide-driven exchange and gravitational circulation exchange along the SRE
during spring tide, the flushing rate for each estuarine segment was plotted against the river discharge (Fig. 9). The
tidal exchange was dominant over gravitational circulation
exchange near the mouth (SEG1-3) during spring tide where
the flushing rate was about constant for all river discharges.
The flushing rate data were relatively sparse at the oceanic
end member as the small fluctuation of the denominator of
Eq. (3) yielded large scale flushing rate. Although the standard deviation was large, the fitting provides a constant value
of F indicating tide-driven dispersive flux of salt which was
supported by the calculation of potential energy anomaly (see
in discussion) and estuarine parameter ν (=1.04). Tide-driven
dispersive flux dominated over gravitational circulation exchange in transporting salt landward of 7 km from the mouth
of SRE during spring tide due to the larger tidal amplitude
of the spring cycle. McCarthy (1993), Savenije (1993, 2005)
and Nguyen et al. (2008) reported that the gravitational circulation is weak near the mouth of exponentially varying estuary, and tide-driven exchange is dominant. On the basis of
the stratification parameter, well-mixed conditions were also
found near the mouth of the SRE during spring tide (Shaha
and Cho, 2009), where the large tidal amplitude enhanced the
turbulent mixing. Moreover, the tidal dominancy appeared in
the observations of the variations in the diurnal salinity taken
at CTD station 7 with low (28 m3 s−1 ) and high (120 m3 s−1 )
river discharges during spring tide, as shown in Fig. 3. In
both river discharge cases, the same salinity of 27 psu appeared at CTD station 7 during high tide (Fig. 3a and b). This
indicates that the tide was dominant in pushing the salinity of
27 psu from Gwangyang bay to the observation point, where
the freshwater input was negligible.
Hydrol. Earth Syst. Sci., 14, 1465–1476, 2010
1472
D. C. Shaha et al.: Flushing rate for gravitational circulation and tidal exchanges
Fig. 9. Plot of the flushing rate (F ) against the river discharge
(R) for various segments of the Sumjin River Estuary during spring
tide. The intercept value, Fint , indicates the tidal exchanges. The
amounts in excess of the Fint value for various river discharges indicate gravitational circulation exchange (here expressed by Gc ).
Gravitational circulation exchanges entirely dominate at the upstream end.
Fig. 10. Plot of the flushing rate (F ) against the river discharge
(R) for various segments of the Sumjin River Estuary during neap
tide. The intercept value, Fint , indicates the tidal exchanges. The
amounts in excess of the Fint value for various river discharges indicate gravitational circulation exchange (here expressed by Gc ).
Gravitational circulation exchanges entirely dominate at the upstream end.
The combined contribution of tidal exchange and gravitational circulation exchange were found in segments 4 to 10
during spring tide (Fig. 9), where the SRE shows partially
stratified condition on the basis of the stratification parameter (Shaha and Cho, 2009) and also as a function of potential
energy anomaly. Gravitational circulation exchange and tidedriven dispersive flux were differed with the salt content rate
of change for various river discharges. Tide-driven dispersive flux of salt dominated at low river discharge (10 m3 s−1 )
condition in these segments. Fram et al. (2007) found that
tide-driven dispersive flux of salt exceeds gravitational circulation during a period of decreasing river discharge. However, gravitational circulation exchange exceeded tide-driven
dispersive flux at river discharge of 50 m3 s−1 in the upper
segments (SEG6-11). As the M2 tidal amplitude decreased
by 12% within the estuary relative to the mouth (Table 1),
the consequent reduction in the vertical mixing and increasing river discharge enhanced gravitational circulation by increasing potential energy on the water column. Due to the
decrease in tidal amplitude, the gravitational circulation has
intensified in Ariake bay (Yanagi and Abe, 2005). As a con-
sequence, the combined contribution of tidal exchange and
gravitational circulation exchange were important in transporting salt landward of 8 km. In contrast, gravitational flux
was much more effective in transporting salt to segment 11
and 12 during spring tide, which is governed by the river
flow. Savenije (1993) and Nguyen et al. (2008) also found
that gravitational circulation exchange is dominant in the upstream part.
The combined contribution of tidal exchange and gravitational circulation exchange were also found in transporting salt from segment 1 to 10 during neap tide (Fig. 10).
The weaker turbulence during neap tide accelerated the gravitational circulation exchange along the SRE. As a consequence, both tidal exchange and gravitational circulation exchange were important in transporting salt upstream. Tidedriven dispersive flux of salt was also dominant over gravitational flux during neap tide at river discharge of 10 m3 s−1 .
Gravitational circulation exchange was dominant over tidal
exchange along the SRE during neap tide at river discharge
of 50 m3 s−1 . This indicates that strong gravitational circulation exchange was strongly linked to both the stratification
Hydrol. Earth Syst. Sci., 14, 1465–1476, 2010
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D. C. Shaha et al.: Flushing rate for gravitational circulation and tidal exchanges
Fig. 11. Spatial variation of median estuarine parameter (ν) during
spring and neap tides along the Sumjin River Estuary. For ν ∼ 1, upestuary transport of salt entirely by tide-driven mixing. For ν ∼ 0,
up-estuary salt transport almost entirely by gravitational circulation.
For 0.1 < ν < 0.9, both gravitational circulation and tide-driven circulation contribute to transporting salt up-estuary.
Fig. 12. Spatial variation in the potential energy anomaly during
spring and neap tides along the Sumjin River Estuary. Each contour is the average of twelve samples obtained from August 2004 to
April 2007.
5
Discussion
5.1
and the tide (neap). Strong stratified conditions were found
during neap tide along the SRE as a function of the stratification parameter (Shaha and Cho, 2009) and the potential
energy anomaly in the water column. Pulsing of stratification
and gravitational circulation is easily understood in terms of
the significant reduction in vertical mixing during neap tide
due to the weakened effect of the bottom friction (Monismith
et al., 1996). Gravitational circulation exchange was entirely
dominant in transporting salt to segment 11 during neap tide,
which is governed by the river flow.
The estuarine parameter ν (Hansen-Rattray parameter),
as determined from Eq. (4), obviously illustrates which exchange process is responsible in transporting salt up-estuary.
On the basis of the estuarine parameter ν (Fig. 11), the tidedriven dispersion was almost constant landward of 6 km from
the mouth of the SRE during spring tide where ν > 0.9. This
length is consistent with the observed median tidal excursion length of 6.8 km (Shaha and Cho, 2009) where gravitational circulation ceased and the upstream transport of salt
was entirely dominated by tide-driven dispersion (Fig. 9,
SEG1-3). From 7 to 19 km both gravitational circulation and
tide-driven dispersive fluxes had contributions in transporting salt during spring tide (Fig. 9, SEG4–11) where 0.1 <
ν < 0.9. Both gravitational circulation and tide-driven dispersive fluxes were also important in transporting salt from
1 to 19 km during neap tide where 0.1 < ν < 0.9. Landward of 20 km gravitational circulation exchange was much
more effective than tide-driven dispersion during spring and
neap tides where ν < 0.3. MacCready (2004) found ν = 0 at
the upstream end and ν ∼ 0.8 near the mouth of the Hudson River Estuary. The results of Savenije (1993), MacCready (2004) and Nguyen et al. (2008) are consistent with
this calculation.
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1473
Exchange processes based on potential energy
anomaly
The horizontal density gradient has important implications in
generating tidally varying stratification and gravitational circulation (Savenije, 2005). Strong stratification events are periods of intense gravitational circulation (Monismith, 1996)
which are linked through straining of the salinity field. Tidal
straining is the result of velocity shear acting on a horizontal density gradient creating oscillations in the stratification
of the water column (Murphy et al., 2009). To determine
the influence of tidal straining on water column stratification, which is strongly linked with gravitational circulation,
the potential energy anomaly φ of the water column for each
CTD cast was calculated. Following the approaches of Simpson et al. (1990) and de Boer et al. (2008), the potential energy anomaly is the amount of work necessary to completely
mix the water column (Jm−3 ) which can be calculated from
φ=
1
H
Z0
gz(ρ − ρ)dz
(9)
−H
with the depth average density
1
ρ=
H
Z0
ρdz
(10)
−H
where ρ is the vertical density profile over the water column
of depth H , z is the vertical coordinate and g is the gravitational acceleration (9.8 ms−2 ). For a given density profile, φ
(Jm−3 ) represents the amount of work required to completely
mix the water column.
Variations in the tidal exchange and gravitational circulation exchange naturally arise through neap-spring variations
in the presence of the potential energy anomaly along the
SRE. Figure 12 depicts the spatial variation in the potential energy anomaly φ during spring and neap tides along
the SRE. Each contour of the spring and neap tides was the
Hydrol. Earth Syst. Sci., 14, 1465–1476, 2010
1474
D. C. Shaha et al.: Flushing rate for gravitational circulation and tidal exchanges
average for twelve samples obtained from August 2004 to
April 2007. The strength of tide-driven mixing and stratification varied significantly between the spring and neap tides,
up to approximately 20 km landward, as a function of φ.
The amount of φ was less than 10 Jm−3 during spring tide
near the mouth (landward of 7 km) of the SRE due to tidally
driven turbulent mixing (Fig. 12). Burchard and Hofmeister (2008) have examined the dynamics of the potential energy anomaly at a location, where the water column is fully
destabilized during flood, with a range of φ between 0 and
9 Jm−3 . Therefore, it can be assumed that tide-driven exchange may be dominant, when φ is <10 Jm−3 . In addition,
the tidal exchange zone extends roughly a tidal excursion
from the mouth (Signell and Butman, 1992). The median
tidal excursion observed in the SRE was 6.8 km (Shaha and
Cho, 2009), that indicating the tidal exchange zone. Signell
and Butman (1992) also found rapid exchange in the tidal
mixing zone. As per the stratification parameter, well-mixed
conditions were found near the mouth (landward about 7 km)
of the SRE during spring tide (Shaha and Cho, 2009), that
also indicating the tidal exchange zone. Thus, the tidal exchange zone, as determined from the flushing rate near the
mouth during spring tide, is consistent with the function of
φ, stratification parameter and tidal excursion.
In contrast, the amount of φ increased to 10∼24 Jm−3 during spring tide landward of 7 km from the mouth. The water
column contained more φ in the central and inner regimes of
the SRE relative to the mouth due to the reduction in mixing
as the M2 tidal amplitude decreased by 12% within the estuary (Table 1). As a consequence, both gravitational circulation exchange and tide-driven exchange were important in
transporting salt in the central and inner regimes of the SRE
(landward of 7 km) under various river discharge conditions.
Increased values of φ in the water column (27 < φ <
67 Jm−3 ) represents stronger stratification during neap tide
than during spring tide. The weaker turbulence during a neap
tide could lead to the reduction in mixing and the consequent
increase of φ in the water column enhanced gravitational circulation. Both gravitational circulation exchange and tidedriven exchange were contributed in transporting salt into
the SRE. Gravitational circulation exchange is not necessarily proportional to the potential energy anomaly in the water
column. The dynamics of the potential energy anomaly has
examined by Burchard and Hofmeister (2008) on a strongly
stratified water column, where gravitational circulation exchange exists over the whole tidal period, with a range of φ
between 45 and 60 Jm−3 . The link between stratification and
gravitational circulation develops during neap tide due to the
significant reduction in vertical mixing, which is the result of
the weakened bottom friction (Nunes Vaz et al., 1989; Monismith et al., 1996).
There was no substantial amount of φ required to completely mix the water column landward of 20 km, where
gravitational circulation exchange was entirely dominant in
transporting salt during spring and neap tides (Fig. 11). This
Hydrol. Earth Syst. Sci., 14, 1465–1476, 2010
Table 3. chlorophyll-a concentration in the Sumjin River Estuary
(Park et al., 2005).
Station
chlorophyll-a concentration (µgL−1 )
CTD23
CTD21
CTD15
CTD11
CTD8
CTD2
2.5 ∼ 18.2
3.7 ∼ 108.9
3.0 ∼ 44.4
3.8 ∼ 45.2
2.5 ∼ 48.5
2.8 ∼ 23.7
also indicates that the tidal effects decreased at landward of
20 km from the mouth, and the combined effects between
tidal exchange and gravitational circulation exchange started
from this location. Thus, the tidal exchange and gravitational circulation exchange, calculated using the flushing
rate, showed consistency with the function of potential energy anomaly.
5.2
Effects of exchange processes on spatial heterogeneity of chlorophyll-a
The flushing rate for the entire SRE could not provide information about the connections between the transport and
spatial heterogeneity of non-conservative quantities such as
chlorophyll-a. Conversely, the calculation of the flushing
rate for multiple segments of the SRE provided strong clues
about the importance of transport processes in shaping the
spatial patterns of chlorophyll-a. Park et al. (2005) conducted a study on spatiotemporal fluctuations in the abundance of the demersal copepod, Pseudodiaptomus sp., in
the SRE during spring tide. The chlorophyll-a concentrations measured during their research period are shown in
Table 3. The concentrations were lowest at upstream end
where salt transport almost entirely by gravitational circulation (Shaha and Cho, 2009). As gravitational circulation exchange may increase in strength with increasing river flow,
advective transport of estuarine resident populations will increase (Monismith et al., 2002). Owing to this advective
loss, the chlorophyll-a concentration was lowest at upstream
end segment. However, the chlorophyll-a concentration was
highest at the distance of 20 km due to the advection by the
river flow from upstream end. This region is the landward
limit of haline stratification as a function of φ where there is
no net landward and seaward movement of water. As a result, Pseudodiaptomus sp. maintained their positions in this
region.
Conversely, lower concentration of chlorophyll-a was also
found near the mouth of the SRE during spring tide. Strong
tide-driven exchange was found near the mouth during spring
tide (Figs. 7, 9, 11 and 12), which caused advection of planktonic organisms from the mouth of the SRE to Gwangyang
bay. As a result, the concentration was lower near the mouth.
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D. C. Shaha et al.: Flushing rate for gravitational circulation and tidal exchanges
Hydrodynamic conditions, such as tide-driven exchange and
gravitational circulation exchange, are entirely different during spring and neap tides in the SRE. Therefore, a study on
the abundance of the demersal copepod, Pseudodiaptomus
sp., should be conducted during neap tide, as the SRE is
strongly stratified during neap tide that inhibits vertical migration of planktonic organisms.
6
Conclusions
Single flushing rate of the SRE did not show the spatial variation of exchange characteristics. To investigate spatial and
spring-neap variations of gravitational circulation and tidedriven exchanges the flushing rate was calculated between
multiple segments of the SRE and the adjacent bay. The
tides caused rapid exchange in the vicinity of the mouth during spring tide compared to neap tide. The stratification and
water column stability was found to vary in different sections of the SRE as a function of potential energy anomaly
which modulated gravitational circulation and tide-driven exchanges.
The tide-driven dispersion was dominant at low river discharge condition along the SRE during spring and neap tides.
Tide-driven dispersive flux of salt was also dominant near the
mouth (landward of 7 km) during spring tide for all river discharge conditions observed due to the larger tidal amplitude
where gravitational circulation ceased. However, both gravitational circulation and tidal exchanges were contributed in
transporting salt in the central and inner regime during spring
tide due to the reduction in tidal amplitude that caused partially stratified conditions. The combined contributions of
two fluxes were also appeared during neap tide along the
SRE. Gravitational circulation exchange entirely dominated
for salt flux at the upstream end during spring and neap tides.
These results furnished strong clues about the spatially
varying abundance of planktonic organisms in the SRE. Results suggested the use of spatially varying flushing rate to
estimate tide-driven and gravitational circulation exchanges,
and also to understand the distributions of living biomass and
suspended particles in an estuary.
Acknowledgements. This research was supported by the NAP
program of the Korea Ocean Research Development Institute and
the project titled “Dynamics and prediction of long-term ocean
climate variability” funded by MLTM. The helpful comments of
H. H. G. Savenije, an anonymous reviewer and P. A. G. Regnier
substantially improved this manuscript. The authors would like to
acknowledge the members of the Earth Environment Prediction
Laboratory for their enthusiastic supports during the data collection.
Edited by: P. Regnier
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1475
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